Regularization of Divergent Integrals in Boundary Integral Equations for Elastostatics

Abstract

Let consider a homogeneous, linearly elastic body, which in three-dimensional (3-D) Euclidean space ℝ3 occupies volume V with smooth boundary ∂V The region V is an open bounded subset of the 3-D Euclidean space ℝ3 with a C0,1 Lipschitzian regular boundary ∂V The boundary contains two parts \(\partial V_u\) and \(\partial V_p\) such that \(\partial V_u \cap \partial V_p = \emptyset \mbox{and} \partial V_u \cup \partial V_p = \partial V\) On the part \(\partial V_u\) are prescribed displacements ui(x) of the body points and on the part \(\partial V_p\) are prescribed tractions pi(x), respectively. The body may be affected by volume forces bi(x). We assume that displacements of the body points and their gradients are small, so its stress-strain state is described by the small strain deformation tensor εij(x) Then differential equations of equilibrium in the form of displacements may be presented in the form